A combinatorial view of Andrews' proof of the L-M-W conjectures
type: Item
instance of: scholarly article
title: A combinatorial view of Andrews' proof of the L-M-W conjectures
zbMATH Open document ID: 0614.05006
DOI: 10.1016/S0195-6698(85)80047-0
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: The authors provide combinatorial proofs of some identities already proved analytically by \textit{G. Andrews} [Partitions, q-series, and the Lusztig-Macdonald-Wall conjectures, Invent. Math. 41, 91-102 (1977; Zbl 0354.20006)]. The combinatorial setting is lattice paths which the authors say stems from formal language methods, most particularly the work of Flajolet and Viennot. (There are references given in the paper under review.) In fact, the procedure can be used to attack lattice path interpretations to sequences of polynomials defined by difference equations with polynomial coefficients. The authors indicate that their methods have many applications to problems dealing with the theory of partitions. No doubt, this paper is the first of a series in which interesting combinatorial interpretations are attached to partition identities. This paper should be studied by combinatorialists who work with generating functions.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 3993592
zbMATH Keywords: lattice path interpretations
zbMATH Keywords: difference equations
zbMATH Keywords: partition identities
zbMATH Keywords: generating functions
Wikidata QID: Q123273696
author: Adriano M. Garsia
author: Jeffrey Remmel
reviewed by: David A. Klarner
MaRDI profile type: Publication
cites work: Partitions, \(q\)-series and the Lusztig-MacDonald-Wall conjectures
cites work: Q3937409
cites work: On the conjugacy classes in the unitary, symplectic and orthogonal groups
full work available at URL: s0195-6698(85)80047-0
OpenAlex ID: W1964375672
description: scientific article; zbMATH DE number 3993592